The Standard Identities (a+b)2, (a-b)2 are a set of two complementary identities that relate the squares of the sums and differences of two numbers. These i...
The Standard Identities (a+b)2, (a-b)2 are a set of two complementary identities that relate the squares of the sums and differences of two numbers. These identities can be used to simplify expressions and solve mathematical problems.
(a+b)2 = a2 + 2ab + b2
(a-b)2 = a2 - 2ab + b2
These identities can be derived using the following steps:
Start with the definition of the square of a number: a2 = a * a.
Apply the definition of the square of a sum: (a+b)2 = (a+b)(a+b) = a2 + 2ab + b2.
Apply the definition of the square of a difference: (a-b)2 = (a-b)(a-b) = a2 - 2ab + b2.
The Standard Identities are useful in simplifying expressions, solving quadratic equations, and analyzing geometric figures. They can also be used to express complex numbers in the form a + bi